Package com.opttek.optquest

Class COptQuestTDistribution

java.lang.Object
com.opttek.optquest.COptQuestTDistribution
All Implemented Interfaces:
com.opttek.optquest.IProbabilityDistribution
public class COptQuestTDistribution extends Object implements com.opttek.optquest.IProbabilityDistribution

  • Constructor Summary

    Constructors
    Constructor
    Description
    COptQuestTDistribution(double df)
     

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cdf(double x)
     
    static double
    CDF(double t, double df)
    Student's t-Distribution Cumulative Distribution Function (CDF) Computes P(T ≤ t) where T follows a t-distribution with df degrees of freedom.
    double
    chaz(double x)
     
    double
    haz(double x)
     
    double
    pdf(double x)
     
    static double
    PDF(double t, double df)
    Student's t-Distribution Probability Density Function (PDF) Computes the probability density at t for a t-distribution with df degrees of freedom.
    double
    ppf(double x)
     
    static double
    PPF(double p, double df)
    Student's t-Distribution Percent Point Function (PPF) - Inverse CDF Computes the value t such that P(T ≤ t) = p, where T follows a t-distribution with df degrees of freedom.
    double
    sf(double x)
     

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • COptQuestTDistribution

      public COptQuestTDistribution(double df)

  • Method Details

    • pdf

      public double pdf(double x)
      Specified by:
      pdf in interface com.opttek.optquest.IProbabilityDistribution

    • cdf

      public double cdf(double x)
      Specified by:
      cdf in interface com.opttek.optquest.IProbabilityDistribution

    • ppf

      public double ppf(double x)
      Specified by:
      ppf in interface com.opttek.optquest.IProbabilityDistribution

    • sf

      public double sf(double x)
      Specified by:
      sf in interface com.opttek.optquest.IProbabilityDistribution

    • chaz

      public double chaz(double x)
      Specified by:
      chaz in interface com.opttek.optquest.IProbabilityDistribution

    • haz

      public double haz(double x)
      Specified by:
      haz in interface com.opttek.optquest.IProbabilityDistribution

    • CDF

      public static double CDF(double t, double df)
      Student's t-Distribution Cumulative Distribution Function (CDF) Computes P(T ≤ t) where T follows a t-distribution with df degrees of freedom. Uses the relationship: CDF(t, df) = 0.5 * I_x(df/2, 1/2) where I_x is the regularized incomplete beta function and x = df/(df + t²).
      Parameters:
      t - the value at which to evaluate the CDF
      df - degrees of freedom (must be positive)
      Returns:
      the cumulative probability P(T ≤ t)

    • PDF

      public static double PDF(double t, double df)
      Student's t-Distribution Probability Density Function (PDF) Computes the probability density at t for a t-distribution with df degrees of freedom. Formula: f(t; ν) = Γ((ν+1)/2) / (√(νπ) * Γ(ν/2)) * (1 + t²/ν)^(-(ν+1)/2)
      Parameters:
      t - the value at which to evaluate the PDF
      df - degrees of freedom (must be positive)
      Returns:
      the probability density at t

    • PPF

      public static double PPF(double p, double df)
      Student's t-Distribution Percent Point Function (PPF) - Inverse CDF Computes the value t such that P(T ≤ t) = p, where T follows a t-distribution with df degrees of freedom. Uses normal approximation for initial guess when df > 1000, then applies Newton-Raphson iteration for refinement.
      Parameters:
      p - the probability (must be between 0 and 1, exclusive)
      df - degrees of freedom (must be positive)
      Returns:
      the value t such that CDF(t, df) = p